Cosine-Sine Decomposition

This topic describes LAPACK driver routines for computing the cosine-sine decomposition (CS decomposition). You can also call the corresponding computational routines to perform the same task.

The computation has the following phases:

  1. The matrix is reduced to a bidiagonal block form.
  2. The blocks are simultaneously diagonalized using techniques from the bidiagonal SVD algorithms.

Table "Driver Routines for Cosine-Sine Decomposition (CSD)" lists LAPACK routines (FORTRAN 77 interface) that perform CS decomposition of matrices. The corresponding routine names in the Fortran 95 interface are without the first symbol.

Computational Routines for Cosine-Sine Decomposition (CSD)

Operation

Real matrices

Complex matrices

Compute the CS decomposition of a block-partitioned orthogonal matrix

orcsd uncsd

Compute the CS decomposition of a block-partitioned unitary matrix

orcsd uncsd

For more complete information about compiler optimizations, see our Optimization Notice.